Digital communication requires the transmission of data symbols. For frequency modulation (FM), each symbol defines a change in the frequency of the transmitted signal or, as indicated in FIG. 1 to which reference is now made, as a set of changes in the frequency.
FIG. 1 shows two Manchester encoded bits. When using FM, a "1" bit has the frequency of f.sub.0 +.DELTA.f during the first T/2 seconds (from t.sub.0 to t.sub.1 of FIG. 1) of the bit and the frequency of f.sub.0 -.DELTA.f during the second T/2 seconds (from t.sub.1 to t.sub.2) of the bit. A "0" bit has the opposite shape: during the first T/2 seconds (from t.sub.2 to t.sub.3) of the bit the frequency is f.sub.0 -.DELTA.f and during the second T/2 seconds (from t.sub.3 to t.sub.4) of the bit the frequency is f.sub.0 +.DELTA.f. For advanced mobile phone service (AMPS) wideband data transmission, the bit duration T is 0.1 msec (i.e. bit rate is 10 KHz) and .DELTA.f is 8 KHz.
Attempts have been made to decode the symbol values using the in-phase i(t) and quadrature q(t) components of the baseband version of the complex transmitted signal, where: